Reciprocal coevolving interactions between hosts and parasites are a primary source of strong selection that can promote rapid and often population- or genotype-specific evolutionary change. These host-parasite interactions are also a major source of disease. Despite their importance, very little is known about the genomic basis of coevolving host-parasite interactions, particularly in nature. Here, we use gene expression and molecular sequence evolution approaches to take critical steps towards characterizing the genomic basis of interactions between the freshwater snail Potamopyrgus antipodarum and its coevolving sterilizing trematode parasite, Microphallus sp., a textbook example of natural coevolution. We found that Microphallus-infected P. antipodarum exhibit systematic downregulation of genes relative to uninfected P. antipodarum. The specific genes involved in parasite response differ markedly across lakes, consistent with a scenario where population-level coevolution is leading to population-specific host-parasite interactions and evolutionary trajectories. We also identified a set of rapidly evolving loci that present promising candidates for targets of parasite-mediated selection across lakes as well as within each lake population. These results constitute the first genomic evidence for population-specific responses to coevolving infection in the P. antipodarum-Microphallus interaction and provide new insights into the genomic basis of coevolutionary interactions in nature.